Stability Analysis Of Neural Networks With Time-varying Delays

Delayed neural networks are extensively applied in those fields such as signal processing, moving imagine processing, artifical intelligence, global optimizing and so on. Since the dynamical characteristics of delayed neural networks include stable, unstable, oscillatory behaviors, the dynamics of delayed neural networks have attracted a great deal of attention in recent years. Many interesting results on the global stability, for example, absolute stability, asymptotic stabilty, robust stability and exponential stability of delayed neural networks have been obtained.In this thesis, the problem of stability analysis is considered for some classes of neural networks with time-varying dealy. The main results are as follows:First, the stability analysis for a class of recurrent neural networks with a time-varying delay in a range is studied. Both delay-independent and delay-dependent conditions are derived. For the former, an augmented Lyapunov functional is constructed and the derivative of the state is retained. It can be easily extended to handle neural networks with polytopic uncertainties. For the latter, a new type of delay-range-dependent condition is proposed using the free-weighting matrix technique to obtain a tighter upper bound on the derivative of the Lyapunov-Krasovskii functional.Second, a novel method on the exponential stability analysis of cellular neural networks with time-varying delays is proposed. The delay center point method, which divides the delay interval into two sub-intervals by introducing its center point, is utilized. A more general Lyapunov-Krasovskii functional is constructed to derive a delay-dependent exponential stability criterion by employing different weighting matrices for different sub-intervals.Finally, the exponential stability analysis for a class of cellular neural networks with both interval time-varying delays and general activation functions is concerned. The boundedness assumption of the activation function is not required. The limitation on the derivative of time delay being less than one is relaxed and the lower bound of time-varying delay is not restricted to be zero.